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mathslover
 3 years ago
Prove that if the 3 altitudes of a triangle are equal then the triangle is equilateral.
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mathslover
 3 years ago
Prove that if the 3 altitudes of a triangle are equal then the triangle is equilateral. See attachment

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mathslover
 3 years ago
Best ResponseYou've already chosen the best response.1I tried to do this and have got so far that AB = AC

mathslover
 3 years ago
Best ResponseYou've already chosen the best response.1I took following triangles :ABF and AEC by AAS I got both of these triangles congruent and therefore by CPCT AB = AC

mathslover
 3 years ago
Best ResponseYou've already chosen the best response.1(CPCT = Congruent Parts of Congruent Triangles are equal)

joemath314159
 3 years ago
Best ResponseYou've already chosen the best response.1That idea should work to get that AB=BC as well.

mathslover
 3 years ago
Best ResponseYou've already chosen the best response.1So far , we have got ABC as isosceles. Now, I took triangle ABC and AFC both of these triangles are congruent by RHS BF = FC ( by CPCT ) therefore F is mid point of BC an AF is median and altitude also Therefore , this is the property of an equilateral triangle , so ABC is an equi. triangle

mathslover
 3 years ago
Best ResponseYou've already chosen the best response.1You mean to take ABE and BEC triangles @joemath314159 ?

joemath314159
 3 years ago
Best ResponseYou've already chosen the best response.1yep. and do exactly what you did with the other triangles again.

mathslover
 3 years ago
Best ResponseYou've already chosen the best response.1I meant this : ADC and ABD in the above comment.

mathslover
 3 years ago
Best ResponseYou've already chosen the best response.1I think I had tried that earlier but I didnt' get any favorable result , wait let me do it again

joemath314159
 3 years ago
Best ResponseYou've already chosen the best response.1there are many combinations you could take. The pair I see is triangles BEC and BDA.

mathslover
 3 years ago
Best ResponseYou've already chosen the best response.1Oh yes that will work ... BEC and BDA .. this gives some output to me.

mathslover
 3 years ago
Best ResponseYou've already chosen the best response.1Thanks a lot @joemath314159 for your help .. Might gonna work in more concentration for me..
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